Question
se the image to answer the question.
Two parabolas with a common vertex are drawn on a coordinate plane. The x-axis ranges from negative 3 to 3 in one-unit increments and the y-axis ranges from negative 4 to 2 in one-unit increments.
Which of the following best describes the transformation from the solid-line graph to the dotted-line graph and correctly states the factor k?
(1 point)
Responses
horizontal stretch with a factor k = 0.5
horizontal stretch with a factor k = 0.5
horizontal stretch with a factor k = 2
horizontal stretch with a factor k = 2
horizontal compression with a factor k = 0.5
horizontal compression with a factor k = 0.5
horizontal compression with a factor k = 2
Two parabolas with a common vertex are drawn on a coordinate plane. The x-axis ranges from negative 3 to 3 in one-unit increments and the y-axis ranges from negative 4 to 2 in one-unit increments.
Which of the following best describes the transformation from the solid-line graph to the dotted-line graph and correctly states the factor k?
(1 point)
Responses
horizontal stretch with a factor k = 0.5
horizontal stretch with a factor k = 0.5
horizontal stretch with a factor k = 2
horizontal stretch with a factor k = 2
horizontal compression with a factor k = 0.5
horizontal compression with a factor k = 0.5
horizontal compression with a factor k = 2
Answers
GPT-4o mini
To determine the correct transformation from the solid-line graph to the dotted-line graph, we need to analyze the changes in the parabolas.
1. **Horizontal Stretch vs Compression**:
- A horizontal stretch (factor > 1) makes the graph wider, whereas a horizontal compression (factor < 1) makes the graph narrower.
2. **Identifying the Factor \( k \)**:
- A horizontal stretch occurs when the x-coordinates of the points on the graph are multiplied by a factor smaller than 1, while a horizontal compression occurs when these points are multiplied by a factor greater than 1.
If we assume that the dotted-line graph is visually narrower than the solid-line graph, it means that the transformation is a horizontal compression. Conversely, if the dotted-line graph appears wider than the solid-line graph, the transformation would be a horizontal stretch.
Given the options you provided, if the dotted-line graph looks narrower than the solid-line graph, the correct description would be:
**horizontal compression with a factor k = 0.5.**
If the dotted-line graph looks wider than the solid-line graph, then the correct description would be:
**horizontal stretch with a factor k = 2.**
Without the actual image to reference, I cannot definitively determine which transformation applies. If the dotted line is narrower, choose "horizontal compression with a factor k = 0.5." If it is wider, choose "horizontal stretch with a factor k = 2."
1. **Horizontal Stretch vs Compression**:
- A horizontal stretch (factor > 1) makes the graph wider, whereas a horizontal compression (factor < 1) makes the graph narrower.
2. **Identifying the Factor \( k \)**:
- A horizontal stretch occurs when the x-coordinates of the points on the graph are multiplied by a factor smaller than 1, while a horizontal compression occurs when these points are multiplied by a factor greater than 1.
If we assume that the dotted-line graph is visually narrower than the solid-line graph, it means that the transformation is a horizontal compression. Conversely, if the dotted-line graph appears wider than the solid-line graph, the transformation would be a horizontal stretch.
Given the options you provided, if the dotted-line graph looks narrower than the solid-line graph, the correct description would be:
**horizontal compression with a factor k = 0.5.**
If the dotted-line graph looks wider than the solid-line graph, then the correct description would be:
**horizontal stretch with a factor k = 2.**
Without the actual image to reference, I cannot definitively determine which transformation applies. If the dotted line is narrower, choose "horizontal compression with a factor k = 0.5." If it is wider, choose "horizontal stretch with a factor k = 2."